{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DW3D4GA3D3ANM4YMZGBOILPSYI","short_pith_number":"pith:DW3D4GA3","canonical_record":{"source":{"id":"1206.3852","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-06-18T08:55:40Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"4ef82283cd4dfcbbcbb1854a1aaaad63af2f9397a0c3172b63c219963c90a548","abstract_canon_sha256":"8116bf69cdf7750175e36379ef4b5bfdd2df28dbc35ea0ec7cbf80c08dc97419"},"schema_version":"1.0"},"canonical_sha256":"1db63e181b1ec0d6730cc982e42df2c23ea0269ff2ba55ee2adbc95410d5e091","source":{"kind":"arxiv","id":"1206.3852","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3852","created_at":"2026-05-18T01:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3852v3","created_at":"2026-05-18T01:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3852","created_at":"2026-05-18T01:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"DW3D4GA3D3AN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DW3D4GA3D3ANM4YM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DW3D4GA3","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DW3D4GA3D3ANM4YMZGBOILPSYI","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3852","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-06-18T08:55:40Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"4ef82283cd4dfcbbcbb1854a1aaaad63af2f9397a0c3172b63c219963c90a548","abstract_canon_sha256":"8116bf69cdf7750175e36379ef4b5bfdd2df28dbc35ea0ec7cbf80c08dc97419"},"schema_version":"1.0"},"canonical_sha256":"1db63e181b1ec0d6730cc982e42df2c23ea0269ff2ba55ee2adbc95410d5e091","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:51.854060Z","signature_b64":"H3I5qivaMf1g9T9YFQt22wjvSwLvLxfNQriRwIgwT2YpDo9tP/HuTq3rVxnHiiQBybOyQ/4ptxKMCExN4CH6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1db63e181b1ec0d6730cc982e42df2c23ea0269ff2ba55ee2adbc95410d5e091","last_reissued_at":"2026-05-18T01:56:51.853503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:51.853503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3852","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEsM/o7bSO9nZnju0tyqrUB7R6Kl9iQ2qdO+XzjOmmfpuVsuDxBqUVY8y/0YijzKmmb4e6xQzXZvLMXZJBgABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:53:25.167265Z"},"content_sha256":"c2e68f94267761b5ac8162f2eaf6f8ea96bcfa7ca1835418667cc1fb8492d388","schema_version":"1.0","event_id":"sha256:c2e68f94267761b5ac8162f2eaf6f8ea96bcfa7ca1835418667cc1fb8492d388"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DW3D4GA3D3ANM4YMZGBOILPSYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cosmological perturbations in Massive Gravity and the Higuchi bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","gr-qc"],"primary_cat":"hep-th","authors_text":"Andrew J. Tolley, Matteo Fasiello","submitted_at":"2012-06-18T08:55:40Z","abstract_excerpt":"In de Sitter spacetime there exists an absolute minimum for the mass of a spin-2 field set by the Higuchi bound m^2 \\geq 2H^2. We generalize this bound to arbitrary spatially flat FRW geometries in the context of the recently proposed ghost-free models of Massive Gravity with an FRW reference metric, by performing a Hamiltonian analysis for cosmological perturbations. We find that the bound generically indicates that spatially flat FRW solutions in FRW massive gravity, which exhibit a Vainshtein mechanism in the background as required by consistency with observations, imply that the helicity z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3852","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HrQDpQiCV43fbri2MRm1gC1MAQ9WvXX/v/o/FVj3fvFlSc+VfJcKMxWzIV2abFv2+qX+uyxI5C0SZcbw5JLkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:53:25.167991Z"},"content_sha256":"b92a06adcf91014f08f347bdfd1779dcd81ca4d9a204b820c1300f345cf1be88","schema_version":"1.0","event_id":"sha256:b92a06adcf91014f08f347bdfd1779dcd81ca4d9a204b820c1300f345cf1be88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DW3D4GA3D3ANM4YMZGBOILPSYI/bundle.json","state_url":"https://pith.science/pith/DW3D4GA3D3ANM4YMZGBOILPSYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DW3D4GA3D3ANM4YMZGBOILPSYI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T03:53:25Z","links":{"resolver":"https://pith.science/pith/DW3D4GA3D3ANM4YMZGBOILPSYI","bundle":"https://pith.science/pith/DW3D4GA3D3ANM4YMZGBOILPSYI/bundle.json","state":"https://pith.science/pith/DW3D4GA3D3ANM4YMZGBOILPSYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DW3D4GA3D3ANM4YMZGBOILPSYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DW3D4GA3D3ANM4YMZGBOILPSYI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8116bf69cdf7750175e36379ef4b5bfdd2df28dbc35ea0ec7cbf80c08dc97419","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-06-18T08:55:40Z","title_canon_sha256":"4ef82283cd4dfcbbcbb1854a1aaaad63af2f9397a0c3172b63c219963c90a548"},"schema_version":"1.0","source":{"id":"1206.3852","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3852","created_at":"2026-05-18T01:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3852v3","created_at":"2026-05-18T01:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3852","created_at":"2026-05-18T01:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"DW3D4GA3D3AN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DW3D4GA3D3ANM4YM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DW3D4GA3","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:b92a06adcf91014f08f347bdfd1779dcd81ca4d9a204b820c1300f345cf1be88","target":"graph","created_at":"2026-05-18T01:56:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In de Sitter spacetime there exists an absolute minimum for the mass of a spin-2 field set by the Higuchi bound m^2 \\geq 2H^2. We generalize this bound to arbitrary spatially flat FRW geometries in the context of the recently proposed ghost-free models of Massive Gravity with an FRW reference metric, by performing a Hamiltonian analysis for cosmological perturbations. We find that the bound generically indicates that spatially flat FRW solutions in FRW massive gravity, which exhibit a Vainshtein mechanism in the background as required by consistency with observations, imply that the helicity z","authors_text":"Andrew J. Tolley, Matteo Fasiello","cross_cats":["astro-ph.CO","gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-06-18T08:55:40Z","title":"Cosmological perturbations in Massive Gravity and the Higuchi bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3852","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c2e68f94267761b5ac8162f2eaf6f8ea96bcfa7ca1835418667cc1fb8492d388","target":"record","created_at":"2026-05-18T01:56:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8116bf69cdf7750175e36379ef4b5bfdd2df28dbc35ea0ec7cbf80c08dc97419","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-06-18T08:55:40Z","title_canon_sha256":"4ef82283cd4dfcbbcbb1854a1aaaad63af2f9397a0c3172b63c219963c90a548"},"schema_version":"1.0","source":{"id":"1206.3852","kind":"arxiv","version":3}},"canonical_sha256":"1db63e181b1ec0d6730cc982e42df2c23ea0269ff2ba55ee2adbc95410d5e091","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1db63e181b1ec0d6730cc982e42df2c23ea0269ff2ba55ee2adbc95410d5e091","first_computed_at":"2026-05-18T01:56:51.853503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:51.853503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H3I5qivaMf1g9T9YFQt22wjvSwLvLxfNQriRwIgwT2YpDo9tP/HuTq3rVxnHiiQBybOyQ/4ptxKMCExN4CH6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:51.854060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3852","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2e68f94267761b5ac8162f2eaf6f8ea96bcfa7ca1835418667cc1fb8492d388","sha256:b92a06adcf91014f08f347bdfd1779dcd81ca4d9a204b820c1300f345cf1be88"],"state_sha256":"e7e79eec9620b3692a245836bfc6ebb6f019838d5086527a26fcdb99e9fc4315"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l7HZkBDC8kDFqi71Wmq0wBtx6SWRkRihy3Q+GG68IcuzerPFSV2oT5ZR9qgIjLLx04KDT2X3WfrR0YbzGayiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T03:53:25.171456Z","bundle_sha256":"fea15be1d0f6f1018c166b1fa0a67c0a931b11be6de05e96e0a35fcf5e449feb"}}